A fellow photographer recently asked me to help with some film he shot - after shooting a roll of Cinestill800T he forgot to change the ISO setting for his camera and managed to shoot 4 rolls (!) of 100 ISO color film. Yikes. That's a 3-stop underexposure, or about 1/8th the amount of light normally needed for proper exposure.
On a digital camera, if you shoot RAW, it might actually be possible to rescue those images. Digital sensors are quite sensitive to low-light and it's simply a case of boosting the captured signal. In contrast, if a digital sensor is maxed out then they don't do as well as the sensor blows the highlights. Film works the other way around - low light usually means that details are lost, whereas negative color and BW emulsions tend to have quite high latitude for overexposure.
If you have under-exposed your film though, all is not lost. With a 1 or maybe 2 stop underexposure you may be able to bring up the image when you print or scan the negatives. For black and white images this often works really well, but color film might have a slight color cast to it. Shadows will be less well defined and colors more "muddy" or muted. And there is also the option of "pushing" the film. Many photographers talk of "pushing" film when they deliberately shoot a slow speed emulsion at a higher ISO (for example, I often push Acros 100 by shooting it at 400 ISO), but to be accurate the "pushing" only occurs during development - otherwise all you've done is under-exposed the film!
To be simple, the final image is the result of an initial photochemical reaction between the film and the light, and a second chemical reaction between the light-activated areas of the film and the developer. So, if you have under-exposed during the first step, you can in theory compensate by over-developing (pushing) the film during the second step. This should bring the overall image density back up to a more normal level, rescue detail in the shadows for example, but also tends to increase overall contrast and may also alter the overall color balance a little. Pushing film can be as simple as simply running the development step for longer, or it may require a higher temperature, or a little bit of both. Thankfully it's not wizardry, and there is plenty of information and guidance out there - in fact Cinestill includes a helpful table of how to push up to 3 stops using their Cs41 developer kit at a range of temperatures, and the Massive Dev Chart is a crowd-sourced repository of information on film development times.
An example of pushed film - here I used a faster shutter speed to avoid blur but of course ended up under-exposing. I pushed 1 stop in development to compensate. Note the cool halation of the candle flame with the 800T film stock. Shannon Merceron modeling.
In the example below I actually made the opposite mistake as my friend - thinking I was in aperture-priority I accidentally shot a whole series at 1/250s when I should have been closer to 1/4000s. That's a massive FOUR STOP overexposure. I recognized my mistake and made the decision to fix the rest of the roll and hope for the best during scanning. I could have under-developed (pulled) the film but there's more risk with that I think. Shorter developing times may result in uneven results and very odd color shifts, and I only had guidance down to -1 stops. I developed the film normally and this was the result - a perfectly usable image that is in fact on display right now at a local art co-op. This is almost entirely due to using a high-quality film stock, Portra160. Cheaper but similar speed color film stocks would have struggled to do as well - and I challenge a digital camera to cope with a 4-stop overexposure at all!
So as you can see, it's not just the photography that differs between film and digital, but also how you manage and process the film AFTER the shoot. I am happy to offer individual and group tuition sessions if anyone wants to drop me a line, and I also offer film developing/scanning services.